Here is a number machine.
input
x 4
a) Work out the output when the input is 6
b) Work out the input when the output is 31
- 5
output

Answer:

1

Step-by-step explanation:

f(x) = 3x^3+kx+9, and the remainder when f(x) is divided by x+2 is -17, then what is the value of k=1

The probability of drawing an orange marble and then a green marble without replacement  is (a) 1/15 .

The probability of drawing an orange marble on the first draw = 2/10 because there are 2 orange marbles out of total of 10 marbles .

After 1 orange marble is drawn, there are 9 marbles left in the box, of which 3 are green.

So, the probability of drawing a green marble on the second draw, given that an orange marble was drawn on the first draw, is 3/9.

⇒ P(orange, green) = P(orange) × P(green | orange was drawn)

⇒ P(orange, green) = (2/10) × (3/9) = 6/90 = 1/15  ;

Therefore , the value of P(Orange , Green) is = 1/15 .

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The given question is incomplete , the complete question is

A box contains 5 purple marbles, 3 green marbles and 2 orange marbles. Draws are made without replacement. P(orange ,green)

(a) 1/15

(b) 2/15

(c) 3/31

(d) 1/5

We cannot make any definitive inferences about the entire school population, however, so the answer is E. None of the above.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The total number of students are 10+11+23+6=50

Based on the survey of 50 students about their preference for an additional sports team, we can observe that lacrosse is the most popular sport among the surveyed students, with 23 supporters.

It is likely that there would be enough interest to form an ice hockey team, as there were 11 supporters.

We cannot make any definitive inferences about the entire school population, however, so the answer is E. None of the above.

Hence, We cannot make any definitive inferences about the entire school population, so the answer is E. None of the above.

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The table shown below represents the results from a sample group of 50 students

surveyed about a preference for an additional sports team.

Sports Team    Number

Gymnastics       10

Ice hockey         11

Lacrosse             23

Swimming           6

If the school has 500 students, what can be inferred from the survey?

A. There would not be enough students to form a 20-person ice hockey

team.

B. About half of the students prefer lacrosse to the other sports.

C. Fewer than ten students in the school prefer swimming to the other

sports.

D. About 10% of the students prefer gymnastics.

E. None of these

Answer:

Step-by-step explanation:

To solve this system of two equations with two variables (x and y), we'll use the substitution method. Here's how:

Solve one of the equations for either x or y, in terms of the other variable. Let's solve the first equation, 2x - 5y = 4, for x:

x = (4 + 5y)/2

Substitute the expression for x from step 1 into the second equation, 4x = 8 + 10y:

4(4 + 5y)/2 = 8 + 10y

Simplify the equation from step 2:

8 + 10y = 8 + 10y

Solve for y by subtracting 8 from both sides:

10y = 10y

Divide both sides by 10 to find the value of y:

y = y

Now that we have the value of y, we can substitute it back into the expression for x from step 1:

x = (4 + 5 *y)/2

So the solution to the system of equations is (x, y) = ((4 + 5 *y)/2, y=y).

Step-by-step explanation:

You would find a the same way as finding B, just backwards

[tex]( {x}^{2} - 1)( {x}^{2} + 5)[/tex]

Distributing we get

[tex] {x}^{4} + 5 {x}^{2} - {x}^{2} - 5[/tex]

Simplifying it...

[tex] {x}^{4} + 4 {x}^{2} - 5[/tex]

Answer:

Step-by-step explanation:

(-4 - 8)/(5 + 1)= -12/6 = -2

Option C

The reflected function across the {x} - axis would be -

g(x) = -2/5 (10)ˣ.

If the function f(x) is reflected across the {x} - axis, then the new function g(x) becomes -

g(x) = - f(x)

Given is the function as -

f(x) = 2/5 (10)ˣ

We can write the reflected function as -

g(x) = - f(x)

g(x) = - {2/5 (10)ˣ}

g(x) = -2/5 (10)ˣ

Therefore,  the reflected function across the {x} - axis would be -

g(x) = -2/5 (10)ˣ.

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A situation in which a quadratic equation cannot be solved using the quadratic formula include the following: A. The right-hand side of the equation is 1.

Generally speaking, the standard form of a quadratic function is given by this mathematical expression;

ax² + bx + c = 0

Where:

Mathematically, the quadratic formula is modeled or represented by this mathematical expression:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

In this context, we can reasonably infer and logically deduce that a quadratic function cannot be solved by using the quadratic formula when the coefficient of the x²-term is equal to zero (0) or when right-hand side of the equation is equal to one (1).

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Answer:

Step-by-step explanation:

inequality form

d≤ 1

Interval Notation:

(−∞,1]

The proportional relationship used to find the distance that the train will travel after m minutes is given as follows:

d = 0.12m.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

Considering that when the input is of 5, the output is of 0.6, the constant of the relationship in this problem is given as follows:

k = 0.6/5

k = 0.12.

Hence the equation is given as follows:

d = 0.12m.

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15) Evaluating the mathematical expression -10 -144/(-12) shows that 144 is being divided by 12 before subtracting 10, following the application of PEMDAS.

16) The value of the algebraic expression is 2.

The evaluation of an expression is finding its value by substituting variables and applying the PEMDAS rule.

PEMDAS means the order of algebraic operations that applies parentheses, exponents, multiplication, division, addition, and subtraction.

-10 -144/(-12)

-10 + (144/12)

-10 + 12

= 2

Thus, we have evaluated the expression to have a value of 2.

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The function table.

table

x f(x)

-4 4(-4)+3 = -16+3 = -13

0 4(0)+3 = 0+3 = 3

2 4(2)+3 = 8+3 = 11

4 4(4)+3 = 16+3 = 19

5 4(5)+3 = 20+3 = 23

What is Function?

A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

We can complete the function table by substituting the given values of x into the rule for f(x) and simplifying in the following table.

Therefore, the completed function table is as follows.

so final table is

x f(x)

-4  -13

0  3

2 11

4  19

5  23

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Answer:

16

Step-by-step explanation:

As the question states, we are counting downwards which means with every interval we are going back -1. Therefore, 17 - 1 = 16

The equation of the rational function with the given features is given as follows:

F(x) = [4(x² + 5x + 4)]/(x² - x - 6).

A rational function is a fraction, in which both the numerator and the denominator contain instances of the variable x.

Considering the x-intercepts, the numerator of the function is defined as follows:

y = a(x + 4)(x + 1)

y = a(x² + 5x + 4).

Considering the y-intercept at (0,4), the leading coefficient a is given as follows:

a = 4.

The vertical asymptotes determine the zeros of the denominator, which is given as follows:

(x + 2)(x - 3) = x² - x - 6.

Hence the function is defined as follows:

F(x) = [4(x² + 5x + 4)]/(x² - x - 6).

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Answer:

2nd answer : it is equivalent but not completely factored

Step-by-step explanation:

the "pulling out" of 3 as factor was completely correct.

but

3(x² - 4) can be further factored.

remember :

(a + b)(a - b) = (a² - b²)

therefore,

(x² - 4) = (x + 2)(x - 2)

and then

3(x + 2)(x - 2)

would be a complete factorization.

Answer: B) The expression is equivalent, but is not completely factored

Step-by-step explanation:

The expression to be added is 9mn +3m² - 12n²

These are expressions having terms, variables, coefficients, factors and constants.

They are also known to be composed of arithmetic operations, such as;

From the information given, we have the expression;

-7 mm + 2m ²+ 3n²

To make it up to 5m² +2mn-9n²., we have

-7mn + 9mn + 2m² + 3m² + 3n² - 12n²

Hence, the expression is 9mn +3m² - 12n²

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Velocity of rock when it hits the ground is -22.9955152 ft/s

Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time

Its position function is s(t) = –25t² + 1.86t

When it reaches back ground s(t) = 25 m/s

Substituting

               s(t) = –25t² + 1.86t = 25

Using the quadratic formula (-b±√b²-4ac)/2a

(-1.86 ±√1.86-4*25*-25)2*25

(-1.86 ±√1.7298+625)50

(-1.86 ±√626.7298)/50

(-1.86÷25)50

(-1.86+25)50 or( -1.86 -25)50

48.14/50 = 0.9628

This figure is taken because its positive

Time = 0.9628 seconds

Now we need to find velocity when it reaches ground, that is velocity after 0.9628 seconds.

Differentiating s(t) equation

   Substituting t = 0.9628 seconds

               v(t) = –25(0.9628)² + 1.86(0.9628)

v(t) = -23.174596 + 0.1790808

Velocity of rock when it hits the ground is -22.9955152 ft/s

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The exact values of the six trigonometric functions of θ are:

sin(θ) = 0

cos(θ) = -√2/2

tan(θ) = 0

csc(θ) = undefined

sec(θ) = -√2

cot(θ) = undefined

The given point (-14,0) lies on the x-axis in the negative x-axis direction. Drawing a line from the origin to this point creates a right triangle with the hypotenuse being the line from the origin to (-14,0), the opposite side being the y-coordinate of (-14,0), and the adjacent side being the x-coordinate of (-14,0). The length of the hypotenuse can be found using the Pythagorean theorem:

h^2 = (-14)^2 + 0^2

h^2 = 196

h = 14√2

Using the definitions of the six trigonometric functions in terms of the opposite, adjacent, and hypotenuse sides of a right triangle, we can find the exact values of these functions for θ:

sin(θ) = opposite/hypotenuse = 0/14√2 = 0

cos(θ) = adjacent/hypotenuse = -14/14√2 = -√2/2

tan(θ) = opposite/adjacent = 0/-14 = 0

csc(θ) = 1/sin(θ) = undefined (since sin(θ) = 0)

sec(θ) = 1/cos(θ) = -√2

cot(θ) = 1/tan(θ) = undefined (since tan(θ) = 0)

Therefore, the exact values of the six trigonometric functions of θ are:

sin(θ) = 0

cos(θ) = -√2/2

tan(θ) = 0

csc(θ) = undefined

sec(θ) = -√2

cot(θ) = undefined

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A graph of the solution to this inequality 2.45 < x ≥ 4.6 is shown in the image attached below.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Next, we would translate the word problem into an algebraic equation as follows;

2.45 < x ≥ 4.6

By splitting, we have the following compound inequality:

x > 2.45

x ≥ 4.6

In this scenario, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Additionally, the graph contains a dashed line because of the greater than (>) symbol.

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x = 415.

Check attached image 1.

So at this point, we know the measures of the angles, in terms of "x", which is a variable. We may use the implicit information in the drawing to find more information. Such as the total measure of the sum of angles DBE and CBE. This total measure equals 90°, we know this because there's a square drawn on the base of both angles. Whenever you see a square drawn at the base of an angle, it means the measure of that angle is 90°, a right angle.

Check attached image 2.

We know that the sum of angles DBE and CBE equal 90°. Hence:

[tex]DBE+CBE=90[/tex]

In terms of variable "x", this is:

[tex](0.1x-22)+(0.3x-54)=90[/tex]

[tex]0.1x-22+0.3x-54=90[/tex]

[tex]0.1x+0.3x-54-22=90\\ \\0.4x-76=90[/tex]

[tex]0.4x-76+76=90+76\\ \\0.4x=166[/tex]

[tex]\frac{0.4x}{0.4} =\frac{166}{0.4} \\ \\x=415[/tex]

To see if "x = 415" is the correct answer, take the original equation, substitute "x" by "415" and, if the same number appears on both sides of the equal (=) sign, then we've found our answer!

[tex](0.1x-22)+(0.3x-54)=90\\ \\(41.5-22)+(124.5-54)=90\\ \\(19.5)+(70.5)=90\\ \\90=90[/tex]

x = 415.

The measures of the center or variability that are greater than 5 degrees are :

The mean of the data on temperature this week and the last is :

= ( 4 + 10 + 6 + 9 + 6 ) / 5

= 7 degrees Fahrenheit 4+ 10+ 6+9+ 6

The mean of the data on temperature last week and the last is :

= ( 13 + 9 + 5 + 8 + 5 ) / 5

= 8 degrees Fahrenheit

The range of this week's temperature is :

= 10 - 4

= 6 degrees Fahrenheit

All these measures of center are above 6 degrees.

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The full question is:

Temperatures for 5 Days This Week and Last Week

Low Temperatures This Week (Degrees Fahrenheit) 4 10 6 9 6 Low Temperatures Last Week (Degrees Fahrenheit) 13 9 5 8 5 Which measures of center or variability are greater than 5 degrees? Select three choices.

a) the mean of this week’s temperatures

b) the mean of last week’s temperatures

c) the range of this week’s temperatures

d)the mean absolute deviation of this week’s temperatures

e) the mean absolute deviation of last week’s temperatures

Answer: T=Q/p+1

Step-by-step explanation:

Rearrange

Answer:

Step-by-step explanation:

1. YES

2. NO

3.NO

4. YES

1. This is because only some shoes are new not all of them.\

2. There are some new shoes so it is wrong.

3. Not all of them are new

4. Not every shoe is new because there are some old shoes.

1,755 cm² icings are needed for one cake.

The correct option is (C).

What is the area of the circle?

The area of a circle is the amount of space enclosed within the circle. It is a measure of the size of the circle, and it is determined by the distance from the center of the circle to its edge (which is the radius). The formula for the area of a circle is:

A = πr²

The surface area of the circular top of the cake can be found using the formula for the area of a circle:

A = πr^2

where A is the area of the circle, and r is the radius. For the red velvet cake, the radius is 13 cm, so the area of the circular top of the cake is:

A = 3.14 x 13^2 = 530.66 cm^2 (rounded to two decimal places)

To find the surface area of the curved side of the cake, we need to find the circumference of the circular base and multiply it by the height of the cake. The circumference can be found using the formula:

C = 2πr

where C is the circumference and r is the radius. For the red velvet cake, the circumference of the circular base is:

C = 2 x 3.14 x 13 = 81.64 cm (rounded to two decimal places)

So, the surface area of the curved side of the cake is:

A = C x h = 81.64 x 15 = 1224.60 cm^2 (rounded to two decimal places)

Therefore, the total surface area of the cake that needs to be iced (excluding the circular bottom) is:

530.66 + 1224.60 = 1755.26 cm^2 (rounded to two decimal places)

Rounding to the nearest square centimeter, we get that approximately 1755 cm^2 of icing is needed for one red velvet cake at the Bisecting Bakery.

Therefore, 1,755 cm² icings are needed for one cake.

The correct option is (C).

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find derivative of e^(e^x)

use chain rule to find d/dx of e^x is e^x.

so chain rule finds the value e^(e^x) d/dx = e^(e^x) x e^x

simplify to e^[(e^x)+x]

The length of the dotted line would be 7.922 ft.

A circle's diameter is measured from the center of the circle outward. It is equivalent to twice the radius, or the distance a circle's radius is measured from its center to any other point on the circle.

The mathematical formula for a circle's diameter is d = 2r if d is the circumference and r is the radius.

When we subtract the circle's thickness from its outer diameter to determine the provided circle's inner diameter, we obtain q = 17.708 - 4.893 - 4.893.

We can solve this for q = 7.922

The dotted line would be 7.922 feet long as a result.

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The product of a non-zero rational and an irrational number is always irrational number.

To prove this statement:

Let x be a rational number and y be an irrational number.

Let xy=a.

Let us assume that a is rational.

Since, a is rational it can be expressed as  p/q , where p and q are integers.

Let x= m/n , where m and n are integers.

Now, xy=a

[tex]\frac{my}{n} = \frac{p}{q}[/tex]

On cross multiplying we get,

y = pn/qm​

Now, pn and qm are integers.

Hence, pn/qm is a rational number.

However, y is irrational.

Hence, our assumption is incorrect.

Hence, the product of a non-zero rational and an irrational number is always an Irrational number.

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The domain of the relation include the following: C. {-5, -2, 0, 1, 4}.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left of the graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain:

Domain = {-5, -2, 0, 1, 4}.

In conclusion, the domain of this relation are all the x-values (independent value) that are located on the x-axis of the graph, which include {-5, -2, 0, 1, 4}.

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